Polynomial reconstruction of electric charge distribution on the conductive plate caused by external electric field

Effects of external electric and magnetic fields on the linear and nonlinear optical properties of InAs cylindrical quantum dot with modified Pöschl-Teller and Morse confinement potentials

Theoretical and Practical Studies on Effects of External Electrostatic Electric Field on Nucleation and Growth Kinetics of Protein Crystals

In this work, we use Lewenstein’s theory to calculate the high order harmonic spectra of CO molecule in a linearly polarized laser field combined with an external electrostatic field. The results show that the characteristics of the high order harmonic spectra of CO molecule depend strongly on the direction of the external static electric field relative to the orientation of CO. Especially, when the direction of the external static electric field points from O to C, the plateau of the harmonic spectrum becomes wider and the cutoff frequency reaches a larger value than the scenario without external static electric field. When the direction of the external static electric field points from C to O, the harmonic spectrum shows a double-plateau structure. Using Lewenstein theory, these phenomena can be understood from the viewpoint that the harmonic generation comes from a coherent superposition of the contributions of two kinds of channels characterized by C-end ionization and O-end ionization. The C(O)-end ionization channel means that the electron is ionized from C(O) end, then accelerated by the driving electric field, finally recombines with its parent molecular ion at either C or O end, emitting the harmonics. For the same harmonic order, the contribution of the C-end ionization channel is greater than that of the the O-end ionization channel. The two kinds of channels emit harmonics in adjacent half period of laser, where the external static electric field causes the cutoff frequency of the harmonic spectrum to increase and decrease in the adjacent half period of the laser field. Especially, when the direction of external static electric field is from the C to O, the cutoff frequency of the harmonic spectrum of the C-end ionization channel decreases, resulting in a higher first plateau in the spectrum. While, the increase of cut-off frequency of the O-end ionization channel will result in a lower second plateau. When the direction of external static electric field is reversed, the cutoff frequency of the harmonics of the C-end channel increases, leading the plateau of CO harmonic spectrum to become wider than that without the external static electric field. The cut-off frequency of the O-end ionization channel decreases. Because the contribution of the O-end ionization channel can be ignored compared with that of C-end ionization channel, the C-end channel dominates the contribution to harmonic generation and hence there is only one plateau in the harmonic spectrum. This work provides a clear physical picture for the formation of a double-plateau structure of CO harmonic spectra under the action of an external static electric field.

In this chapter, we discuss the fundamentals of electron transport in static external electric and magnetic fields in vacuum and dense media. By “static” and “external” is meant that macroscopic \(\vec E\) and/or \({\mathbf{\vec B}}\) fields are set up in the region where the electron transport is taking place. For example, a high-energy particle detector may be placed in a constant magnetic field so that the momentum of charged particles may be analyzed. The external fields are considered to be static in the sense that they do not change with time during the course of the simulations. This is not a fundamental constraint, but is imposed for simplicity. The bulk of the discussion concerns the theoretical viability of performing electron transport in dense media in the presence of external fields. The trajectories of particles in this case can be quite complicated. The particles can be subjected to a myriad of forces — de-accelerations due to inelastic processes with orbital electrons and nuclei, elastic deflections due to attraction or repulsion in the nuclear electric field, accelerations or de-accelerations by the external electric field, and deflections by the external electric and magnetic fields.

SO2 is not only an important resource but also a notorious air pollutant, so it has attracted increasing attention nowadays. This paper focuses on the influence of external electric field on SO2. In order to obtain more reliable results, the density functional theory B3P86 method is chosen to calculate the values mentioned below. The ground states of SO2 molecule under different strong electric fields ranging from -0.04 a.u. to 0.04 a.u. are optimized by density functional theory B3P86 method with 6-311++g(3d,p) basis sets. The geometric parameters, charge distributions, total energies, dipole moments, the highest occupied molecular orbital (HOMO) energies, the lowest unoccupied molecular orbital (LUMO) energies, energy gaps of SO2 under different external electric fields are obtained, respectively. On the basis of optimized configuration, the excitation energy, transition wavelength and oscillator strength in the same intense external electric field are calculated by the time dependent density functional theory (TD-B3P86) method.#br#The calculated values for geometric parameters of SO2 without external electric field agree well with the available experimental data and other theoretical results. The geometric parameters and charge distribution of SO2 strongly depend on the intensity and direction of external electric field. The total energy of SO2 in the considered range of external electric field first increases and then decreases. On the contrary, the dipole moments of SO2 in different external electric fields ranging from -0.04 a.u. to 0.04 a.u. first decrease and then increase. When the external electric field is -0.04 a.u., the total energy and symmetry of SO2 both reach the maximum values. With the change of external electric field, the LUMO energy first increases and then decreases. The HOMO energy is found to decrease through the variation of the external field. The energy gaps of SO2 are proved to first increase, and then decrease with the variation of external electric field. Through studying the energy gaps of SO2, it is found that the external electric field can affect the chemical reactivity of SO2. The excitation energies, transition wavelengths and oscillator strengths are very complicated with the change of the external electric field. The excitation properties of SO2 molecule are seriously affected by the external electric field.

For pt.I see ibid., vol.43, no.6, pp.1150-9 (1996). An exact solution of the electrostatic problem for calculating the surface charge and electric field distributions in an arbitrary periodic interdigital transducer (IDT) is given using the results of our companion paper. An arbitrary external electric field may be specified along the electrode structure with the unit cell containing one electrode, or several electrodes, of different widths. The potentials of the electrodes that may be specified are also arbitrary. It is shown that in the case without an external field, the solution includes all the known results as special cases. The case of shorted electrodes in the external electric field is investigated in detail. The surface charge and electric field distributions are calculated for a spatially harmonic external field with an arbitrary wavenumber. The results of the calculations are represented graphically for various ratios between the period of the electrode structure and the wavelength of the external field for the case of a unit cell containing one or two electrodes of different widths.

The spatial field distribution is the most frequent subject of standard electrostatic analysis. In this paper the system of several conducting strips is embedded in external spatial- harmonic electric field causing the charge distribution on them. The solution is constructed as a linear combination of certain template functions, evaluated in spectral domain and satisfying the electric boundary conditions on the strips. The problem is analogous to wave scattering; this justifies the application of the wave-scattering terminology (i.e. 'incident wave' for the external field and the corresponding 'radiation conditions') in the considered nonstandard 'electrostatic scattering' problem. The strip total charge and the Bloch harmonics of the 'scattered' field are evaluated. proper one because of its poor numerical accuracy resulting from square-root singularities of σ(x) on strip edges. Direct evaluation of charge spatial spectrum was proposed in work of Danicki (4) for limited number of arbitrary strips without the external electric field. The solution is constructed as a linear combination of certain template functions, being repeated convolutions of Bessel functions, evaluated in spectral domain and satisfying the electric boundary conditions on the strips. The spatial field distribution is only necessary for evaluation of the strip potential and charge integrals in order to formulate the system of equations resulting from the circuit theory (the Kirchhoff's laws). The solution of the one yields the summation coefficients. In the present paper the same template functions are used to build the solution of electrostatic problem for the finite system of arbitrary strips in external electric field. The solution is constructed in spectral domain, and electric field distribution is obtained by inverse Fourier transformation. The problem is referred to as an 'electrostatic scattering,' because this external electric field is assumed to be a spatial harmonic function like that in the electromagnetic scattering problem. The similar problem for infinite periodic system of strips (or groups of strips) was solved in the paper of Danicki (5), where another template functions are defined, which are actually the discrete spectral functions (due to the system periodicity) represented by the Fourier series involving Legendre polynomials Pn. The idea is exploited in this paper for the case of finite non-periodic system of arbitrary strips.

The influence of an external strong electrostatic field on the statistical characteristics of equilibrium free charge carriers in a quasi-two-dimensional structure is considered using an example of an InAs semiconductor quantum film. The analysis is carried out for the case when a strong quantization regime for charge carriers is realized in the film and only the first and second film sub-bands of their quantized motion are occupied. The general analytic expressions for the energy of the quantized motion of charge carriers in a film in the presence of a strong electrostatic field are given. An explicit dependence of the width of the band gap of the sample on the value of the external field is obtained. It is shown that with the increase in the external field, the width of band gap of the sample increases. The calculations and corresponding analytical expressions for the chemical potential, concentration, energy and heat capacity of free charge carriers of an InAs quantum film in the presence of a strong electrostatic field are also presented. It is shown that with an increase in the external electrostatic field, the chemical potential of the system retains its negative sign, but increases by the magnitude. For a given value of the external field, the chemical potential of the system increases linearly with the increase in temperature. It is shown that at a given temperature the carriers’ density decreases with the increase in the external field. At a fixed value of the field, the concentration increases with the increase in temperature. The behavior of the energy and heat capacity of the charge carriers is also determined by the same dependence on the temperature of the system and the magnitude of the external field. It is also shown that the main contribution to the indicated characteristics of the sample is made namely by the first filled sub-band of quantized motion of charge carriers. If the second sub-band is also filled, its contribution to the determination of the statistical characteristics of the sample is exponentially smaller than the contribution of the first filled sub-band.

The paper deals with electromagnetic radiation generated by capillary oscillations of the zero and first modes of oscillations of a droplet in an external electrostatic field. It is assumed that the droplet of an ideal incompressible electrically conductive liquid has a zero total electric charge and that it is charged in an external uniform electrostatic field by induced charges of opposite signs. The radiation under discussion is detected via analytical asymptotic calculations of the second order infinitesimal by the dimensionless amplitude of the droplet oscillations in an external electrostatic field. An analytical expression was found for the intensity of the electromagnetic radiation associated with oscillations of the zero and first modes, and the dependence of the intensity of radiation on the value of the field strength, the droplet size, and the value of the surface tension coefficient.

The theory of atoms in molecules is extended to the case where the molecule is in the presence of an electromagnetic field. This theory is based upon a generalization of quantum mechanics to an open system, as obtained through a corresponding extension of Schwinger’s principle of stationary action. The extension of this principle is possible only if the open system satisfies a particular boundary condition, one which is expressed as a constraint on the variation of the action integral. This is the condition that it be bounded by a surface of zero flux in the gradient vector field of the charge density, the definition of an atom in a molecule. It is shown that this boundary constraint again suffices to define an atom as a quantum subsystem when the molecule is in the presence of an electromagnetic field. The mechanics of an open system and its properties are determined by the fluxes in corresponding vector current densities through its surface. As in the fieldfree case, the obtainment of these currents from the variation of the action integral is a direct result of the variation of the atomic surface and of the imposition of the variational constraint on its boundary. The currents in this case consist of a paramagnetic and a diamagnetic contribution, currents whose presence are a necessary requirement for the description of the properties of a system in the presence of external fields. The variational statement of the Heisenberg equation of motion obtained from the principle of stationary action is used to derive the Ehrenfest force and virial theorems for an atom in a molecule in the presence of external electric and magnetic fields. In this case, there are forces acting on the interior of the atom which arise from the magnetic pressures acting on its surface. It is shown that the molecular electric polarizability and magnetic susceptibility, like other properties, are rigorously expressible as a sum of atomic contributions.

We present a theoretical study of resonant elastic photon scattering by highly charged ions in the presence of external electric and magnetic fields. Special emphasis is placed on head-on collisions of relativistic ion beams and counterpropagating laser photons, as can be observed in ion storage ring experiments. If the collision zone for such a scenario is exposed to a moderate field of a dipole magnet, a fast-moving ion will be subjected to strong electric and magnetic fields in its rest frame due to the Lorentz transformation. To investigate the effect of these fields we performed detailed calculations for the elastic photon scattering by He-like Ca ions moving with the Lorentz factor γL=2395. Such a scenario is of particular interest for the Gamma Factory project which is supported by the CERN Physics Beyond Colliders framework. Based on the results of our calculations, we argue that even moderate magnetic fields significantly modify the rate of detected photons as well as their emission pattern and polarization. This sensitivity to external fields opens interesting avenues for diverse applications for the Gamma Factory project, such as resonance condition tuning, beam cooling, and polarization control. Published by the American Physical Society 2025

The response of the global and local reactivity density-based descriptors (chemical potential, hardness, softness, Fukui function, and local softness) in the presence of external electric field has been studied for some of the simple prototype molecular systems. In addition to the analysis on the reactivity of these systems, the influence of the electric field on the interaction energy of the complexes formed by these systems has also been studied using the recently proposed semiquantitative model based on the local hard-soft acid-base principle. By using the inverse relationship between the global hardness and softness parameters, a simple relationship is obtained for the variation of hardness in terms of the Fukui function under the external electric field. It is shown that the increase in the hardness values for a particular system in the presence of external field does not necessarily imply that the reactivity of the system would be deactivated or vice versa.

The operation of surface plasmon amplifier by stimulated emission of radiation (spaser) in the presence of external optical field is analyzed. The range of external field amplitude E and mismatch Δ of the external field frequency and the spaser generation frequency (Arnold tongue) E > E synchr(Δ) in which the spaser works at the external field frequency is determined. The analytical and numerical calculations at the given mismatch Δ yield three ranges: E < E synchr(Δ) (the spaser exhibits stochastic regime and point (Δ, E) is outside the Arnold tongue), E synchr(Δ) < E < E L (Δ) (transient range where the spaser polarization weakly depends on the field amplitude and is mainly determined by the pump level), and E > E L (the spaser generation is suppressed and the spaser polarization is equal to the polarization of nanoparticle in the presence of external field).

Monopoles, confinement and deconfinement in lattice compact QED in (2+1)D with external fields

The recent discovery of borospherene B40 marks the onset of a new class of all-boron fullerenes. External electric field can influence the structure and property of molecule. It is necessary to understand the electrostatic field effect in the borospherene B40. In this work, density functional theory method at the PBE0 level with the 6-31G* basis set is used to investigate the ground state structures, mulliken atomic charges, the highest occupied molecular orbital (HOMO) energy levels, the lowest unoccupied molecular orbital (LUMO) energy levels, energy gaps, electric dipole moments, infrared spectra and Raman spectra of borospherene B40 under the external electric field within the range of values F=0-0.06 a.u.. The electronic spectra (the first 18 excited states contain excited energies, excited wavelengths and oscillator strengths) of borospherene B40 are calculated by the time-dependent density functional theory method (TD-PBE0) with the 6-31G* basis set under the same external electric field. The results show that borospherene B40 can be elongated in the direction of electric field and B40 molecule is polarized under the external electric field. Meanwhile, the addition of external electric field results in lower symmetry (C2v), however, electronic state of borospherene B40 is not changed under the external electric field. Moreover, the calculated results show that the electric dipole moment is proved to be increasing with the increase of the external field intensity, but the total energy and energy gap are proved to decrease with the increase of external field intensity. The addition of external electric field can modify the infrared and Raman spectra, such as the shift of vibrational frequency and the strengthening of infrared and Raman peaks. Furthermore, the calculated results indicate that the external electric field has a significant effect on the electronic spectrum of borospherene B40. The increase of the electric field intensity can lead to the redshift of electronic spectrum. With the change of the electric field intensity, the strongest excited state (with the biggest oscillator strength) can become very weak (with the small oscillator strength) or optically inactive (with the oscillator strength of zero). Meanwhile, the weak excited state can become the strongest excited state by the external field. The ground state properties and spectral properties of borospherene B40 can be modified by the external electric field. Our findings can provide theoretical guidance for the application of borospherene B40 in the future.